Hello there
First of all, a piece of advice: if you don't want people messing and poking around your Mac, activate the Guest User account, everything is deleted after logging out and is a limited account, where they can't mess your stuff.
Now to your question, Are you sure yours is the only account with administrator privileges? because if this other account was created also as an administrator account (and not a standard) they can make changes on their own and I don't think you can do much about it.
Now if it's a standard account, first of all logout of all accounts (that other account also has to be logged out in order for you to be able to change its password).
After logging out, log back in, open system preferences --> Users & Groups and the other account should be below yours and not greyed out, so you should be able to reset its password.
Good luck
